fabrication of split-rings via stretchable colloidal

Fabrication of Split-Rings via Stretchable Colloidal LithographyYangjun Cai,†,§ Yang Cao,‡,§ Peter Nordlander,‡ and Paul S. Cremer*,†

†Department of Chemistry, Pennsylvania State University, University Park, Pennsylvania 16802, United States‡Department of Physics and Astronomy, Rice University, 6100 Main Street, Houston, Texas 77005, United States

*S Supporting Information

ABSTRACT: Herein, a facile new patterning method isdemonstrated for creating pairs of split-ring resonators (SRRs)in a scalable manner over large surface areas. This method isbased on a novel variation of colloidal lithography calledstretchable colloidal lithography (SCL), which combinesconventional colloidal lithography and stretchable poly-(dimethylsiloxane) (PDMS) molds. To fabricate SRRs, arraysof circular polystyrene (PS) rings were fabricated byconventional colloidal lithography. The circular ring featurescould be transferred to a PDMS stamp, forming negativefeatures, circular apertures on the stamp. The PDMS stamp was then stretched, thereby transforming the circular apertures intoelliptical ones. By using the stretched PDMS molds for polymer imprinting, elliptical rings with nonuniform heights could befabricated. Each elliptical ring could be transformed into a pair of PS SRRs by controlled O2 reactive ion etching. Through asubsequent chemical wet etching step, PS SRRs could be readily transferred into an underlying gold film. The SRRs exhibitedmultiple modes of polarization-dependent plasmonic resonances in the visible and infrared spectral regions. Experiments andcorresponding theoretical modeling demonstrated that these multiple resonances could be tuned in a predictable manner. Alloptical data compared well with results from electromagnetic simulations.

KEYWORDS: split rings, colloidal lithography, gold, etch, surface plasmon resonance, poly(dimethylsiloxane)

Metamaterials are artificially engineered structures withexotic properties that are not usually found in naturally

occurring materials. Generally, they consist of periodic arrays ofmetallic structures with feature sizes less than the incidentelectromagnetic wavelength. Their optical and electronicproperties are strongly dependent on the geometry of theunit structure rather than the constituent materials.1 Thesearchitectures can manipulate electromagnetic waves insurprising ways and therefore exhibit several extraordinaryproperties, such as negative refraction2 and coherent phenom-ena such as Fano resonances.3 This opens up nascent butexciting potential applications, which affect a broad range offields such as communications, lithography, data storage, lightharvesting, and biomedical device fabrication.4 Along withcircular, square, and triangular shapes, split-ring resonators(SRRs) comprise some of the most common building blocksfor metamaterials. Their ability to give rise to negative refractiveindices (NRI) was first proposed by Pendry in 19995 and thenexperimentally demonstrated in 2001.2 Over the past decade,SRRs have attracted extensive research interest and have foundapplications in sensors,6,7 perfect lenses that beat the diffractionlimit,8 invisibility cloaks,9,10 and photonic absorbers forphotovotaics.11,12

A key challenge to realizing the widespread use of SRRsinvolves fabricating these structures over large areas (∼cm2).This is especially challenging for metamaterials operating in theinfrared or visible range, which require nanometer-scalefeatures. Conventional serial fabrication methods, such as

electron beam lithography (EBL) and focused ion beam (FIB)milling cannot meet this requirement because these techniquesnormally only allow for sample fabrication over areas of 100 ×100 μm2 or smaller. Indeed, trying to use EBL or FIB, to makenanosized SRRs over large areas results in low throughput andhigh costs. Alternatively, laser interference lithography and lasermicrolens array lithography also allows for fabricating large-areananopatterns at high throughput.13−15 However, both of thesetwo methods require laser setup and precise alignment,respectively. Moreover, interference lithography only allowsfor the fabrication of standard periodic patterns, such asnanodots and gratings, and laser microlens array lithographyrequires the use of microlens with precise profiles. As such newefforts need to be put into the development of alternativefabrication methodologies.16 So far, only a limited set of newapproaches for large area/nanoscale fabrication have beendeveloped. Such methods are usually based on colloidallithography,17−22 mechanical nanoskiving,23,24 nanoimprintinglithography,25 and capillary force lithography.26 Among these,nanosphere lithography has particular promise for generatingSRRs over large areas at high-throughput and low-cost.17−21

Recently, we developed a new variation of colloidallithography, called stretchable colloidal lithography (SCL), tofabricate elliptically shaped rings in a scalable manner.27 SCL

Received: November 18, 2013Published: February 4, 2014

Article

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© 2014 American Chemical Society 127 dx.doi.org/10.1021/ph400127g | ACS Photonics 2014, 1, 127−134

pubs.acs.org/journal/apchd5

overcomes a key limitation of conventional colloidal lithog-raphy, which otherwise allows for the fabrication of onlycircular geometries. In this new method, circular polymericrings are first fabricated by using silica particles as templates,and their morphology is subsequently transferred to stretchablepoly(dimethylsiloxane) (PDMS) molds. When the PDMSmolds are stretched, the circularly imprinted ring patternsbecome transformed into ellipses, which can be used as moldsfor generating polymeric and metallic elliptical rings (ERs).27

Herein, we demonstrate that these polymeric ERs can also beexploited to generate SRRs (Figure 1). The geometries andsizes of the SRRs can be readily tuned by varying the etchingconditions. As such, the plasmonic resonance of thesestructures could be tuned in a quantitative manner.

■ EXPERIMENTAL SECTION

Materials. Glass slides (No. 2, 2 × 2 cm2) were purchasedfrom VWR. Polished Pyrex 7740 wafers (2.54 × 2.54 cm2 and0.5 mm thick) were obtained from Precision Glass and Optics(Santa Ana, CA). Aqueous suspensions of silica particles (1 μmin diameter) were purchased from Fisher Scientific. Poly-dimethylsiloxane (PDMS, Sylgard 184) and curing agent wereobtained from Dow Corning. Polystyrene (PS) with amolecular weight (Mw) of 97000 was purchased from ScientificPolymer Products, Inc. (Ontario, NY). Fe(NO3)3·9H2O andthiourea were procured of Fluka.Fabrication of Rings. Figure 1 shows a schematic diagram

of the procedure for generating SRR pairs. First, a PDMS stampwith circular apertures was made by SCL as previouslydescribed.27 This was accomplished by first introducing adispersion of silica particles onto a PS film on a glass slide (1.5× 1.5 cm2), which was pretreated with an O2 plasma(HARRICK PDC-32G, 18 W for ∼30 s, 200 mTorr of O2).The O2 plasma treatment rendered the PS film hydrophilic andtherefore resulted in ordered arrays of assembled particles.Upon drying, the samples were annealed at 130 °C (above thetransition temperature of PS: Tg ∼ 100 °C) for 10 min to formcircular PS rings (Figure 1a and Figure S1 in the SupportingInformation). After removal of the silica particles by sonication,the circular PS ring patterns were transferred onto a PDMSstamp by casting PDMS on the substrate and subsequentlycuring at 70 °C for 6 h (Figure 1b). The PDMS stamp (1 mmin thickness) was released from the substrate (Figure 1c) andthen stretched, thereby transforming the circular apertures intoelliptical ones (Figure 1d). Subsequently, the stretched PDMS

mold was put into conformal contact with a PS film on a Au/Cr(50 nm/5 nm) coated Pyrex glass wafer (∼1.2 × 1.2 cm2) andannealed at ∼130 °C for 10 min (Figure 1e). After releasing thePDMS stamp, boat-like PS ERs of nonuniform height wereformed on the PS film (Figure 1f). Next, the samples weretreated by reactive ion etching (RIE) with oxygen (60 W, 250mTorr, 20 sccm O2; Figure 1g) and subsequent wet etching ofgold (Figure 1h) and O2 plasma (Figure 1i).

Characterization. The PS film thickness spin-coated on theAu layer and the residual film thickness after the formation ofPS ERs was determined by measuring the depth of a scratchusing atomic force microscopy (AFM). AFM was carried outwith a Nanoscope IIIa Multimode scanning probe microscope(Veeco-Digital Instrumentals) in tapping mode. The PS ringstructures and the Au rings were examined by AFM andscanning electron microscopy (SEM, JEOL JSM-7500F).Optical spectra of the Au elliptical rings on glass substrateswere measured with a UV−vis-NIR spectrophotometer(Hitachi U-4100) at normal incidence in transmission modeover a wavelength range of 400−3000 nm. In order toinvestigate the effect of polarization, two polarizers wereinserted into the light path before the sample and the reference.

Simulations. Commercial software (COMSOL Multi-physics 4.2) based on the finite element method has beenused to numerically calculate the optical properties of SRRs. Apair of SRRs is modeled over the calculated region. The far-fieldtransform boundary has been employed to obtain the scatteringcross section. Perfectly matched layer (PML) was applied sothat reflections would not go back into the simulated region.The plots of charge distribution density were generated byusing Gauss’s Theorem at the surfaces of the structures.Johnson and Christy’s dielectric function for gold films28 hasbeen used for all simulations.

■ RESULTS AND DISCUSSION

Fabrication of SRRs. In our previous work, elliptical-shaped PS rings (PS ERs) were fabricated through similarprocedures as shown in Figure 1a−f, in which the residual PSfilm was etched away and the remaining closed PS rings wereutilized as wet-etching resists for generating elliptical Aurings.27 To create SRRs, we began with the elliptically shapedPS rings developed in Figure 1f. Here we extended the RIEtime and therefore not only the residual PS film but also part ofthe PS ERs were etched, as shown in Figure 1g. Due to thenonuniform height of the PS ERs, the closed ERs split upon

Figure 1. Schematic illustration of the procedure for fabricating Au SRRs.

ACS Photonics Article

dx.doi.org/10.1021/ph400127g | ACS Photonics 2014, 1, 127−134128

sufficient etching time along the short axis of the ERs, therebyforming pairs of PS SRRs on the gold film (Figure 1g). Thisstep was followed by chemical wet etching of the gold film byusing an aqueous solution of Fe(NO3)3·9H2O (20 mM) andthiourea (30 mM), adjusted to pH 2.0 by HCl. Here, PS SRRsacted as etch masks, and the gold film was etched in the regionsthat were not covered by the PS (Figure 1h). Finally, theremaining PS was removed by O2 plasma treatment and pairs ofAu SRRs were left behind on the glass substrate (Figure 1i).It should be noted that once a PDMS mold with circular

apertures (Figure 1d) was fabricated, it could be usedrepeatedly to create SRRs. In our experiments, we have usedit for up to 30 times with no noticeable degradation in patternquality. This not only avoids the repeated fabrication of thePDMS mold, but also enhances the repeatability as replicationfrom the same PDMS mold results in highly repeatable PS ERs(Figure 1f). One of the key steps in our fabrication procedure isthe stretching of the PDMS stamp (Figure 1d), which wasreplicated from circular PS rings (see Supporting Informationfor the corresponding SEM images). The replicated PDMSstamp has ordered arrays of circular apertures, which containdepressed circular rings (Figure 2a). The corresponding AFMline profile reveals that the aperture depth is uniform along theperimeter (h0 ∼ 36 nm; Figure 2c). Upon stretching the PDMS

stamp, the apertures exhibit two significant changes. First, thesecircular apertures were transformed into elliptical ones asillustrated schematically in Figure 2e. This is confirmed by theAFM scan of the PDMS stamp in the stretched state (Figure2b).Upon stretching, the diameter of the circular apertures, D0,

increased to DL in the direction parallel to the applied stress (σL= (1 + ε)E, where ε and E are the strain and Young’s modulusof PDMS, respectively (Figure 2e). However, the width in thedirection perpendicular to the applied stress decreased to DS(Figure 2e). Such a decrease was caused by Poisson contractionstress, (σS = (1 − 0.5ε)E). Second, the depth of the aperturesalso changed upon stretching. As can be seen from the lineprofiles of the elliptical apertures (Figure 2d), while the depthat the two ends along the long axis (hL ∼ 38 nm) was close toh0 (∼36 nm), the depth along the short axis (hS ∼24 nm) wasshorter than h0. In other words, when circular apertures arestretched, the apertures for long axes are expanded andmaintain the original depth (left panel in Figure 2f); however,the apertures along the short axes are contracted by a Poissoncontraction stress, leading to a partial collapse at the bottom ofthe apertures (right panel in Figure 2f).With the nonuniform depth, the polymer structures

imprinted from the stretched PDMS stamp exhibit similarnonuniform geometries as shown in Figure 3a. Specifically, it is

lowest along the short axis (green dotted line) and highestalong the long axes (blue dotted line), leading to boat-likestructures. A line profile from the AFM image quantifies theprofile of these boat-like structures, where the two ends of theER along the long axis are ∼25 nm higher than those along theshort axis (Figure 3b). Here the height difference in PS ERs isslightly smaller than the depth difference of the PDMSapertures (i.e., hL − hS), which could be caused by an AFMartifact in measuring deep apertures.As demonstrated above, Au SRRs can be fabricated by

exploiting the nonuniform height of PS ERs, whereby the latteris partially etched away. The height difference (hL − hS) of PSERs between the two axes is the key to the formation of SRRsby subsequent controlled etching. In order to split the closedER in the RIE process, the height along the short axis needs tobe smaller than that along the long axis. Figure S2 shows thevalues of hL and hS for the ERs of different aspect ratios (AR =1.0−2.1), which were fabricated by applying different stresses.Here, AR is defined as the ratio of the outer diameter along thelong axis to that of the outer diameter along the short axis (i.e.,DL/DS). It was found that while the height along long axes (hL)remained almost constant (∼55 nm), the height along shortaxes (hS) decreased with increasing AR up to 1.5 and then

Figure 2. AFM images (5 × 5 μm2) of the PDMS stamp replicatedfrom circular PS rings generated from colloidal lithography (a) beforeand (b) after stretching (stain ∼40%), respectively. (c, d)Corresponding line profiles from (a) and (b), respectively. (e)Schematic illustration of the geometrical transformation from circularto elliptical apertures upon stretching. (f) Schematic illustration of thestretch (left) and collapse (right) of PDMS apertures under theexternal stress (σL) and the induced Poisson contraction stress (σS),respectively.

Figure 3. (a) 3-D (top) and side-view (bottom) AFM images (5 × 5μm2) of the PS ERs. (b) Line profiles of PS ERs along the long andshort axes as indicated in (b).



leveled off. As such, when the AR was 1.0 or 1.2, hL was tooclose to hS, which is not suitable for SRR fabrication. When theAR was above 1.2 (e.g., AR =1.5), the height difference, hL − hS,increases to 20 nm, which was large enough to split the closedring through controlled RIE.We used the PS ERs in Figure 3, which had an AR of ∼1.8

and a height difference of 25 nm, for the fabrication of SRRs.After RIE and wet chemical etching, ordered arrays of Au SRRpairs were obtained on the glass substrate as demonstrated bylow and high magnification SEM images, Figure 4a and b,respectively. In this case, the generated SRRs have a separationdistance (d) between two split ends of 260 ± 55 nm (Figure4b). The height of the Au SRRs are uniform, as expected (∼45nm thick), as evidenced by the AFM line profile shown inFigure 4c.Control of the Geometries of SRRs. The method

described above allows for a high degree of feature tunabilityby varying the size of the silica particles, the annealing time/temperature, the conditions of RIE and the duration of thechemical wet etching step.29,30 Moreover, the AR can be readilytuned by modulating the applied stress,27 resulting in differentgeometries for the SRRs. Below, we will demonstrate that theseparation distance between two SRRs or the size of the SRRscan be easily tuned even after the formation of PS ERs.As shown by the 3D AFM image in Figure 3a, the height of

PS ERs gradually increases from a minimum value along theshort axes to a maximum value along the long axes. Therefore,it should be possible to control the separation distance of SRRpairs simply by varying the RIE time. The height, H(x), of thepolymer ERs above the Au substrate can be treated as the sumof two parts, as illustrated in the inset of Figure 5a. First, thereis a residual PS film above the gold surface in the flat regions ofthe surface, which has a constant thickness (h0 ∼ 40 nm).Second, there is an additional height, h(x), of the PS ellipticalrings above the residual film. h(x) increases gradually as onemoves from the minimum along the short axis to the maximumvalue along the long axis of the elliptical ring, as shown in theinset scheme in Figure 5a. As such, the overall height (H(x) =h0 + h(x)) also increases with the distance (x) away from thecenter of the short axis (Figure 5a). Due to the symmetry of the

ERs, H(x) is approximately identical to H(−x). Therefore, theresulting separation distance, d, approximately equals 2x (i.e., d= 2x; inset scheme of Figure 5a).In Figure 5a, the left-hand y-axis indicates H(x), while the

right-hand y-axis shows the RIE time (t) needed to remove thatcorresponding height of the PS film from the surface. The RIEetching rate, H(x)/t, is approximately 1.8 nm/s, which can bediscerned by noting that the RIE time needed to remove theresidual film (h0 ∼ 40 nm) is ∼22 s (x-axis in Figure 5a). Thistime should also represent an absolute lower bound for thetime needed to fabricate ERs. In practice, it was found that the

Figure 4. (a) Low and (b) high magnification SEM images of pairs of SRRs on a glass substrate. The average gap distance of the SRRs is ∼260 nm.(c) AFM line profile shows that the height of the SRRs is around 45 nm.

Figure 5. Control of the separation distance of SRR pairs. (a) Plot ofthe height of PS ERs (H(x) = h0 + h(x), left y-axis) and thecorresponding O2 RIE time (t, right y-axis) as a function of thedistance (x) away from the center of the short axis. The insetschematic diagram shows the path for the distance (x), the separationdistance (d), and the height of PS ERs (h0 and h(x)). The value of H isthe sum of the thickness of the residual PS film (h0) and the PS ERabove the residual film (h(x)), measured from the AFM images of thePS ERs (e.g., Figure 3a). The right y-axis is the time that is required toetch the corresponding PS thickness at the left y-axis based on the O2RIE rate (vRIE = H(x)/t ∼ 1.8 nm/s). (b) Three representative AFMimages (5 × 5 μm2, scale bars: 1 μm) of SRRs with separationdistances of 627 ± 36, 520 ± 34, and 260 ± 55 nm generated at theRIE times of 40, 43, and 46 s, respectively.



minimum RIE time for obtaining Au SRRs was ∼38 s(horizontal black dash line in Figure 5a). Furthermore, whenthe etching time was increased (40, 43, to 46 s), the separationdistance (d) should correspondingly increase to 280, 500, and650 nm, respectively (see blue, red, and purple arrows in Figure5a). These values are obtained by simply noting the thicknessalong the elliptical rings which needed to be etched away ateach RIE time. Indeed, such predicted values agree very wellwith the experimentally measured values (260 ± 55, 520 ± 34,and 627 ± 36 nm) from the AFM images in Figure 5b. Thus,the etch rate can be used to predict the split ring separationdistance.Optical Spectra of SRRs. After fabrication, the SRRs were

characterized by UV−vis-NIR measurements (400−3300 nm)at the normal incidence. Figure 6a shows the extinction spectra,

measured with unpolarized light, for the three SRR pairs fromFigure 5b. As can be seen, the spectra exhibited broad LSPRpeaks that became less pronounced and even broader as thedistance between SRR pairs increased. Much of the broadeningin these cases should be caused by the nonuniformity in sizes ofthe SRR features as well as the roughness induced during thefabrication process (e.g., chemical wet-etching). In order toimprove the quality of the resonances, we thermally annealedthe SRRs.31,32 For gold, the melting temperature, Tm, is 1337 K(1064 °C)) and the temperature at which the atoms start todiffuse, known as the Tammann temperature (TT ∼ 0.5Tm), is669 K (396 °C).33 Therefore, the annealing temperature wasset to 500 °C, which is well above TT. After thermal annealingat 500 °C for 4 h, we found that the gold surface indeedbecame smoother (Figure S2 in Supporting Information).

Figure 6b−d shows the comparison of the extinction spectra ofthe three different SRRs before and after thermal annealing. Forall three cases, the peaks sharpened substantially. Moreover,some of the resonant peaks were also blue-shifted, which isconsistent with a slight contraction of the length of theseparticles as the edges are rounded.Next, we investigated the origin of the plasmonic resonances

of the SRRs. Figure 7a shows the extinction spectra of the SRRs

(O2 RIE time of 40 s) upon illumination with both unpolarizedand polarized light. In the following, we refer to the twopolarizations as u- and c-polarizations, as defined in Figure 7c.For the c-polarization (c-pol, red line in Figure 7a), theextinction spectrum exhibited three main resonant peakscentered at 2063, 1143, and 586 nm. The strong resonanceat 2063 nm, labeled c1, is associated with the plasmonicresonance along the contour of the C-shaped split ring. Theweaker resonance at 1143 nm, labeled c2, is a higher-ordermode resonance. The third peak, labeled pp(c), can be assignedto a resonance perpendicular to the SRR tips. This resonance isanalogous to particle resonances observed in small goldnanoparticles or disks.18,21,34 For the u-polarization (u-pol,blue line in Figure 7a), only a strong peak, termed u1, appearsat 1267 nm in the spectrum. The highest energy peak for the u-polarization, labeled pp(u), is similarly associated with theresonance perpendicular to the contour of SRRs, which slightlyred-shifted to 650 nm as compared to pp(c). Comparisonbetween the spectra obtained from nonpolarized and polarizedlight indicates that the c1 and u1 resonances observed fornonpolarized light are in agreement with those observed withpolarized light, but the weak c2 resonance overlapped with theu1 resonance in the nonpolarized spectrum.In order to verify the above assignments of the resonances,

the extinction spectra of an SRR pair were simulated by Comsol(Figure 7b). For these simulations, we used a pair of SRRs with

Figure 6. Effect of thermal annealing on the optical spectra of SRRs.(a) Extinction spectra of the as-fabricated SRRs (before thermalannealing) obtained at O2 RIE time of 40, 43, and 46 s. (b−d)Comparison of the extinction spectra of the SRRs obtained at differentRIE times before (green, blue, and maroon lines) and after (black line)annealing.

Figure 7. Experimental (a) and simulated (b) extinction spectra of AuSRRs. The black, red, and blue lines indicate unpolarized and c and u-polarized light, respectively. (c) Schematic diagram of SRRs showingthe c- and u-polarizations and geometries used in simulation. (d)Simulated charge density distributions of different modes andpolarizations. The red and blue arrows surrounding the charge densitydistributions show the instantaneous directions of the inducedcurrents.



a gap distance (d) of 280 nm, which was obtained from an ERwith DL, DS, wL, and wS of 1118, 607, 298, and 140 nm,respectively (see definitions of parameters in Figure 7c). It isobserved that all resonances assigned in experiments (Figure7a) are also present in the simulation and the wavelengths ofthe corresponding resonances agree well with each other. Thesimulated charge density distributions of the correspondingresonances are shown in Figure 7d. In the density distributionplots, red and blue represent two opposite charges (i.e., +ve and−ve) and white represents the standing wave node (neutralpoint). These charge distributions define induced currents inSRRs (arrows surrounding the charge distributions in Figure7d) and the order of the standing waves oscillating in the SRRs.The orders of the modes are defined by the number of nodes(i.e., the white strips in Figure 7d) in the charge densitydistributions. For the c1 mode (1940 nm), there is one node ineach SRR, indicating a dipolar resonance with a mode numberof m = 1. Similarly, because the u1 (1400 nm) and c2 (1000nm) modes have two and three nodes, respectively, their modenumber should be m = 2 and m = 3, as indicated in Figure 7d.In addition, the charge distributions of the pp(c) (740 nm) andpp(u) (760 nm) modes confirm that the resonances are theresult of polarizations of SRRs perpendicular to the two tipsand the contour of the SRRs, respectively.In order to investigate the tunability of resonances by the

RIE time, the extinction spectra of the SRRs fabricated at threedifferent O2 RIE times (40, 43, and 46 s) are plotted in Figure8a. It is clear that resonances of the same polarization and mode

generally blue-shift and decrease in intensity with increasingRIE time (see the dotted arrows in Figure 8a). For all threecases, the wavelengths of the pp(c) resonances are slightlylarger than those of pp(u) resonances. While the pp(c)resonances remain almost fixed at ∼586 nm, the pp(u)resonances do slightly blue-shift with decreasing SRR size. Inaddition, the c2 resonance is only observed for the largestSRRs. To further analyze the experimental results, we simulatedthe extinction spectra for pairs of SRRs for all cases (Figure 8b).

Clearly, all resonances (c1, u1, and c2) exhibited the sametrends observed in the experimental data. Specifically, the sameblue-shifts and decrease in peak size can be observed with theincrease of etching time (dotted arrows in Figure 8b).In order to further understand the microscopic origin of the

SSR resonances, we employed a simple standing-wave modelfor their wavelengths λ:

λ λλ λ=

+⇔ = −⎜ ⎟⎛

⎝⎞⎠L

mn

nLm

( )2

20

effeff 0

(1)

where L is the contour length of the SRR, m is the mode indexof each resonance, neff is the effective refractive index of thesurrounding medium, and λ0 is a constant that depends on thegeometric structure.35,36 We plotted the measured andcalculated λ value as a function of L/m in Figure 8c. As canbe seen, the relationship between these variables is linear forboth the experimental and simulated data. This suggests thatthe standing wave model with its linear relationship between λand L/m can qualitatively explain the tunability of the SRRresonances. The slope obtained from eq 1 is 2neff. In thepresent experiment, with the SRRs surrounded by air and theglass substrate, neff can be approximated as

=+

nn n

2effA2

S2

(2)

where nA and nS are the refractive indices of the air (nA = 1) andthe glass substrate (nS = 1.47),23,37 respectively. This leads to anneff of 1.26. Based on the linear fittings in Figure 8c, the neffvalues are 1.10 and 1.19 for experiments and simulation,respectively. Although these data are slightly smaller thanestimated values, they are in reasonable agreement (i.e., 1.0 <neff < 1.47). Here the slight difference between the experimentsand simulations can be attributed to the uncertainty in neff. Inthe simulations, we used the value estimated from eq 2 where itis assumed that the coverage of the gold feature by the glasssubstrate (nS = 1.47) and air (nS = 1.0) are the same (∼50%).In the experiments, however, the coverage of the glass substrateshould be somewhat less because the vertical walls of the goldSRRs are also covered by air, which would results in a smallerneff.

■ CONCLUSIONWe have demonstrated a new method for generating pairs ofSRRs by the combination of colloidal lithography andmechanical stretching. A pair of SRRs can be obtained fromeach colloidal particle. The geometries of the SRRs, includingthe size and separation distance, could be qualitativelycontrolled by simply varying the RIE time. Arrays of theSRRs gave rise to multiple polarization-dependent resonancesranging in frequency from the visible to NIR. Both theexperimental and simulation data indicated that the tunabilityof the resonances could be explained by a standing wave model,which also provides a simple method to predict the wavelengthsof the SSR resonances. As our method is based on colloidallithography and allows for large-scale fabrication, the fabricatedstructures can provide versatile platforms for plasmonic sensordesign and metamaterials.

■ ASSOCIATED CONTENT*S Supporting InformationSEM images of circular polymer rings; height of PS ERs abovethe residue PS films at the long (hL) and short (hS) axes with

Figure 8. (a, b) Experimental and simulated extinction spectra ofarrays of SRR pairs generated at different O2 RIE times (40, 43, and 46s), as shown in Figure 5b, respectively. In (a) and (b), the red and bluelines indicate c- and u-polarizations, respectively. The red and bluedotted arrows are used to indicate the changes of the resonantwavelengths of the same polarization and mode. (c) Plots ofexperimental (black) and simulated (blue) resonance wavelengths(λ) as a function of L/m. The dash lines are linear fits.



different ARs; comparison of gold surfaces before and afterthermal annealing. This material is available free of charge viathe Internet at http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: [email protected].

Author Contributions§These authors contributed equally to this work (Y.C. andY.C.).

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSP.S.C and Y.C. thank the Norman Hackerman AdvancedResearch Project (NHARP, 010366-0040-2009) from theTexas Higher Education Coordinating Board and the Officeof Naval Research (N00014-08-0467). We thank N. Large forhelpful guidance on modeling calculations. P.N. and Y.C. weresupported by the Robert A. Welch Foundation (C-1222) andthe Office of Naval Research (N00014-10-1-0989).

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fabrication of split-rings via stretchable colloidal

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